In mathematics, the
Dirac delta function, or
function, is a
generalized function, or
distribution, on the real number line that is zero everywhere except at zero, with an
integral of one over the entire real line. The delta function is sometimes thought of as an infinitely high, infinitely thin spike at the origin, with total area one under the spike, and physically represents the density of an idealized
point mass or
point charge. It was introduced by theoretical physicist
Paul Dirac. In the context of
signal processing it is often referred to as the
unit impulse symbol (or function). Its discrete analog is the
Kronecker delta function, which is usually defined on a discrete domain and takes values 0 and 1.